97=2x^2-1

Solution for 97=2x^2-1 equation:

97=2x^2-1

We move all terms to the left:

97-(2x^2-1)=0

We get rid of parentheses

-2x^2+1+97=0

We add all the numbers together, and all the variables

-2x^2+98=0

a = -2; b = 0; c = +98;
Δ = b2-4ac
Δ = 02-4·(-2)·98
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28}{2*-2}=\frac{-28}{-4}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28}{2*-2}=\frac{28}{-4}
=-7
$